Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class CFR121A {

	public static void main(String[] args) {
		long n = new Scanner(System.in).nextLong();
		double k2;
		long t1 = 0, mk1 = Math.round(2*Math.sqrt(n));
		for(long k1=1; k1<mk1; k1++){
			t1 += k1;
			k2 = 0.5*(-1+Math.sqrt(1 + 8*(n-t1)));
			if(Math.round(k2) - k2 == 0 && k2 > 0){
				System.out.println("YES");
				return;
			}
		}
		System.out.println("NO");
	}
}